+937 
Can anyone solve this? (without calculator please) Answer: 0.25
+937 Here's what I tried:
First I looked at 1.75 + sqrt(3) and said, "Well, why not set it equal to a variable?". So I replaced it with x.
Then I got \(2\sqrt{x} - x\), but that didn't help at all. I can't set it equal to anything. I can't solve it with a variable. So then I thought I would just need to solve it by hand. But how in the world would I know what \(\sqrt{3}\) was? Luckily, I remebered that it was 1.732. So, thenI solved it as shown below:
\(2\sqrt{1.75+1.732} - (1.75+1.732)\)
\(=2\sqrt{3.482}-3.482\)
Now what? How do I solve this?
+937 If we squared it, though, we would get 2(sqrt(3.482)), which wouldn't simplify.
+118667 \(2\sqrt{1.75+\sqrt3}-(1.75+\sqrt3)\\ \)
I'm coming up blank.
but sqrt root of 3 is irrational so it is not exactly equal to what you said.
+118667 Finally I got it !!
\(2\sqrt{1.75+\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{4(\frac{7}{4}+\sqrt3)}\qquad -(1.75+\sqrt3)\\~\\ =\sqrt{7+4\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2)^2+(2*2*\sqrt3)+(\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2+\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =(2+\sqrt3)\qquad-(1.75+\sqrt3)\\~\\ =2+\sqrt3-1.75-\sqrt3\\~\\ =0.25\)
Is that impressive or what! LOL
